Conical Projection in plane

How to create a conical beam projection in both 2d and 3d plane.

Answer 1

[Divyam]

Hi @SWETHA MOHANACHANDRAN,

Assuming that you are trying to visualize a cone that emanates from a point and extends outward into 2D or 3D space the "fill" and "plot" functions for the 2D space and the "fill3" and "plot3" functions for the 3D space can be used to visualize the projection.

For 2D space, here is a sample code that provides the projection for the cone's cross section.

% Parameters for the cone
height = 10; % Height of the cone
radius = 3; % Base radius of the cone
numPoints = 50; % Number of points for plotting

% Create the cone
theta = linspace(0, 2*pi, numPoints);
% Parameters for 2D projection
projectionHeight = 5; % Height at which to take the 2D cross-section
scaleFactor = projectionHeight / height; % Scale factor for the radius at this height

% Calculate the 2D projection
x2D = radius * scaleFactor * cos(theta);
y2D = radius * scaleFactor * sin(theta);

% Plot the 2D projection
figure;
fill(x2D, y2D, 'b', 'FaceAlpha', 0.5);
hold on;
plot(0, 0, 'ko', 'MarkerSize', 10, 'MarkerFaceColor', 'k');
xlabel('X-axis');
ylabel('Y-axis');
title('2D Conical Beam Projection');
axis equal;
grid on;

For 3D space, here is a sample code that provides the projection for the cone along the z-axis.

apex = [0, 0, 0]; % Apex of the cone

x = [0, radius * cos(theta)];
y = [0, radius * sin(theta)];
z = [0, height * ones(1, numPoints)];

% Plot the 3D cone
figure;
fill3(x + apex(1), y + apex(2), z + apex(3), 'r', 'FaceAlpha', 0.5);
hold on;
plot3(apex(1), apex(2), apex(3), 'ko', 'MarkerSize', 10, 'MarkerFaceColor', 'k');
xlabel('X-axis');
ylabel('Y-axis');
zlabel('Z-axis');
title('3D Conical Beam');
axis equal;
grid on;
view(3);